Order-7-3 triangular honeycomb: Difference between revisions

Revision as of 19:34, 18 April 2022

Latest revision as of 08:48, 22 August 2025

(9 intermediate revisions by 3 users not shown)

Line 40:

It isa part of a sequence of regular honeycombs with [[heptagonal tiling]] [[vertex figures]]: {''p'',7,3}.

{{-Clear}}

=== Order-7-4 triangular honeycomb===

Line 77:

It has a second construction as a uniform honeycomb, [[Schläfli symbol]] {3,7^1,1}, Coxeter diagram, {{CDD|node_1|3|node|split1-77|nodes}}, with alternating types or colors of order-7 triangular tiling cells. In [[Coxeter notation]] the half symmetry is [3,7,4,1⁺] = [3,7^1,1].

{{-Clear}}

=== Order-7-5 triangular honeycomb===

Line 110:

|}

{{-Clear}}

===Order-7-6 triangular honeycomb===

Line 142:

|[[File:H3_376_UHS_plane_at_infinity.png|240px]]<BR>Ideal surface

|}

{{-Clear}}

===Order-7-infinite triangular honeycomb===

Line 177:

It has a second construction as a uniform honeycomb, [[Schläfli symbol]] {3,(7,∞,7)}, Coxeter diagram, {{CDD|node_1|3|node|7|node|infin|node_h0}} = {{CDD|node_1|3|node|split1-77|branch|labelinfin}}, with alternating types or colors of order-7 triangular tiling cells. In Coxeter notation the half symmetry is [3,7,∞,1⁺] = [3,((7,∞,7))].

{{-Clear}}

=== Order-7-3 square honeycomb===

Line 273:

|}

{{-Clear}}

=== Order-7-3 apeirogonal honeycomb===

Line 341:

|}

{{-Clear}}

=== Order-7-5 pentagonal honeycomb===

Line 375:

|[[File:H3_575_UHS_plane_at_infinity.png|240px]]<BR>Ideal surface

|}

{{-Clear}}

=== Order-7-6 hexagonal honeycomb===

Line 410:

It has a second construction as a uniform honeycomb, [[Schläfli symbol]] {6,(7,3,7)}, Coxeter diagram, {{CDD|node_1|6|node|split1-77|branch}}, with alternating types or colors of cells. In Coxeter notation the half symmetry is [6,7,6,1⁺] = [6,((7,3,7))].

{{-Clear}}

=== Order-7-infinite apeirogonal honeycomb ===

Line 452:

{{reflist}}

*[[H. S. M. Coxeter|Coxeter]], ''[[Regular Polytopes (book)|Regular Polytopes]]'', 3rd. ed., Dover Publications, 1973. {{ISBN|0-486-61480-8}}. (Tables I and II: Regular polytopes and honeycombs, pp.&nbsp;294–296)

* ''The Beauty of Geometry: Twelve Essays'' (1999), Dover Publications, {{LCCN|99035678}}, {{ISBN|0-486-40919-8}} (Chapter 10, [http://www.mathunion.org/ICM/ICM1954.3/Main/icm1954.3.0155.0169.ocr.pdf Regular Honeycombs in Hyperbolic Space] {{Webarchive|url=https://web.archive.org/web/20160610043106/http://www.mathunion.org/ICM/ICM1954.3/Main/icm1954.3.0155.0169.ocr.pdf |date=2016-06-10 }}) Table III

* [[Jeffrey Weeks (mathematician)|Jeffrey R. Weeks]] ''The Shape of Space, 2nd edition'' {{ISBN|0-8247-0709-5}} (Chapters 16–17: Geometries on Three-manifolds I, II)

* George Maxwell, ''Sphere Packings and Hyperbolic Reflection Groups'', JOURNAL OF ALGEBRA 79,78-97 (1982) [http://www.sciencedirect.com/science/article/pii/0021869382903180]

* Hao Chen, Jean-Philippe Labbé, ''Lorentzian Coxeter groups and Boyd-Maxwell ball packings'', (2013)[https://arxiv.org/abs/1310.8608]

Line 463:

* [[Danny Calegari]], [http://lamington.wordpress.com/2014/03/04/kleinian-a-tool-for-visualizing-kleinian-groups/Kleinian Kleinian, a tool for visualizing Kleinian groups, Geometry and the Imagination] 4 March 2014. [https://web.archive.org/web/20161109004910/http://math.uchicago.edu/~dannyc/papers/kleinian_mtf_Feb_2014.pdf]

[[Category:Honeycombs (geometry)3-honeycombs]]

[[Category:Isogonal 3-honeycombs]]

[[Category:Isochoric 3-honeycombs]]

[[Category:Order-7-n 3-honeycombs]]

[[Category:Order-n-3 3-honeycombs]]

[[Category:Regular 3-honeycombs]]